Self-energy catastrophe of the boson-fermion model of high-temperature superconductors

It is known that in the boson-fermion model (BFM) the self-energy of bosons hybridised with fermions prevents Cooper pairing of fermions via virtual transitions into unoccupied bosonic states. The pairing is allowed if and only if the real bosons are condensed. This 'self-energy catastrophe' rules out the BFM as a phenomenological model of superconductivity. We show that an opposite conclusion, recently advocated by some authors, stems from a violation of the energy conservation law. The BFM critical temperature is actually determined by the Bose-Einstein condensation (BEC) temperature of real bosons rather than by a mean-field BCS expression. It appears to be a few orders of magnitude lower than that derived within the mean-freld approximation neglecting the self-energy effect. (C) 1999 Elsevier Science B.V. All rights reserved.